The Open UniversitySkip to content

The hyperbolic geometry of continued fractions K(1|bn)

Short, Ian (2006). The hyperbolic geometry of continued fractions K(1|bn). Annales Academiae Scientiarum Fennicae Mathematica, 31(2) pp. 315–327.

Full text available as:
Full text not publicly available
Due to copyright restrictions, this file is not available for public download
Google Scholar: Look up in Google Scholar


The Stern-Stolz theorem states that if the infinite series ∑|bn| converges, then the continued fraction K(1|bn) diverges. H. S. Wall asks whether just convergence, rather than absolute convergence of ∑bn is sufficient for the divergence of K(1|bn). We investigate the relationship between ∑|bn| and K(1|bn) with hyperbolic geometry and use this geometry to construct a sequence bn of real numbers for which both ∑|bn| and K(1|bn) converge, thereby answering Wall's question.

Item Type: Journal Article
Copyright Holders: 2006 The Author
ISSN: 1239-629X
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Mathematics, Computing and Technology
Item ID: 22452
Depositing User: Ian Short
Date Deposited: 29 Jul 2010 10:47
Last Modified: 25 Feb 2016 05:59
Share this page:

▼ Automated document suggestions from open access sources

Actions (login may be required)

Policies | Disclaimer

© The Open University   + 44 (0)870 333 4340